Concisely state the distribution of X: what is the name of the distribution and

Question

Concisely state the distribution of X: what is the name of the distribution and what are its parameters? According to the 68-95-99.7 rule, 68 percent of IQ scores are within mu plusminus 1 sigma for a normal distribution. This corresponds approximately to what Intelligence Classification? Another school wants to serve the needs of the "middle" 99.7 percent of adults. Use the 68-95-99.7 rule and determine which Intelligence Classifications will be EXCLUDED from classes at this school. What are the individuals? What is the response variable, and its units and type? There are two major tests of readiness for college, the ACT and the SAT. ACT scores are reported on a scale from 1 to 36. The distribution of ACT scores for more than 1 million students in a recent high school graduating class was roughly normal with mean mu = 20.8 and standard deviation sigma = 4.8. SAT scores are reported on a scale from 400 to 1600. The SAT scores for 1.4 million students in the same graduating class were roughly normally distributed with mean mu = 1026 and standard deviation sigma = 209. Tonya scores 1318 on the SAT. Jim scores 27 on the ACT. Assuming that both tests measure the same thing, who has the higher score? Jose scores 1287 on the SAT. Assuming that both test measure the same thing, what score on the ACT is equivalent to Jose's SAT score? Read the article "Study: Birth control pill doesn't make young women gain weight." Answer the following questions about the study What are the individuals? Describe the sample, that is, the type of women, their ages, etc. Describe the population that the study is most likely trying to relate to. How does the sample compare with the population? Do you think this study provides convincing evidence that the pill is not associated with weight gain for young women? Explain. What is one of the response variables and its type? What is the explanatory variable and its type?

Explanation / Answer

PROBLEM 3.

a)

As z = (x-u)/sigma

Then for Tonya,

z = (1318-1026)/209 = 1.397129187

For Jim,

z = (27 - 20.8)/4.8 = 1.291666667

Hence, TONYA HAS A HIGHER SCORE. [ANSWER]

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b)

As z = (x-u)/sigma

Then for Jose,

z = (1287-1026)/209 =1.248803828

Thus, as

x = u + z*sigma = 20.8 + 1.248803828*4.8 = 26.79425837 [ANSWER]

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